α-双对角占优矩阵

Abstract

Li Bishan和Tsatsomeros定义了双对角占优矩阵,并且给出了不可约双对角占优矩阵是奇异的及不是H-阵的充分必要条件。本文利用矩阵的有向图的方法研究了α-双对角占优矩阵的性质,并给出了A为奇异的及A不是H-阵的充分必要条件,推广了其主要结果。

Li Bishan and Tsatsomeros gave the definition of doubly diagonally dominant matrix and presented some necessary and sufficient conditions for an irreducible doubly diagonally dominant matrix to be a sigular matrix or not to be an H-matrix. In this paper,we present some necessary and sufficient conditions in terms of the directed graph for an irreducible a-doubly diagonally dominant matrix to be a singular matrix or not to be an H-matrix,and generalize the related results of Li and Tsatsomeros'.